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Answer on Calculus Question for hsd

Question #16800
You work for Pinstripe Partners LLC, a Cayman Islands based hedge fund founded by one of your fellow students. Your company can both invest and borrow cash at an annual rate of 2% compounded continuously.

(a) You own a derivative contract that will pay out $150 million in 5 years (this
will be the only payment). Your boss instructs you to sell this contract and replace it
with another one which will already pay out in 3 years and which has the same present
value as the existing contract. What will be the sum paid out by the replacement
contract after 3 years?

(b) You have invested $100 million in the company Advantage Electronics Inc.
The value of this investment grows at a rate of 6% per year compounded continuously.
At the same time, you have also invested $80 million in West End Property, growing
at a rate of 8% compounded continuously. After how many years will both investments
have the same value?
Expert's answer
(a) (($15*10^7)/e^(5*.02))*e^(3*.02) = $15*10^7*e^(-2*.02) ≈ $144.1
million

(b) 100e^(.06t) = 80e^(.08t)
.. 100/80 = e^(.02t)
.. Ln(5/4)/.02 = t ≈ 11.157
The two investments will have the same value ($195.3 million) after 11.2
years.

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